Abstract: A computed axial tomography (CAT) system including a ring assembly surrounding a location at which the object is placed; an X-ray source mounted on the ring assembly; an array of X-ray sensors arranged on the periphery of the ring assembly for measuring X-ray intensity from the object; a drive motor for rotating the ring assembly about the object; measurement control circuitry controlling the drive motor, receiving data from the array of X-ray sensors and generating a plurality of vectors of X-ray data therefrom, said plurality of vectors being represented by a measured column tensor; a memory for storing the measured column tensor; and a computer programmed to left multiply the measured column tensor stored in said memory by a reconstruction tensor T to obtain an estimate of a desired measurement column tensor, wherein said reconstruction tensor T is equal to R.sub.dm R.sub.mm.sup.-1, R.sub.

Abstract: A method and apparatus involving the use of a thickness measurement probe having a predetermined resolution to measure the thickness of a wafer over a two-dimensional area of the wafer, the method including sampling the measured thickness of the wafer with the probe to generate an image of the two-dimensional area of the wafer, the image being a two-dimensional array of measurements, each measurement representing a measurement of the thickness of a different region of the two-dimensional area, the two-dimensional array of measurements being represented by a measured column tensor; and left multiplying the measured column tensor by a reconstruction tensor T to obtain an estimate of a desired measurement column tensor, where the reconstruction tensor T is equal to R.sub.dm R.sub.mm.sup.-1, R.sub.dm being a cross-covariance tensor computed for d, a desired measurement column tensor, and m, the measured column tensor, and R.sub.